To make sweet potato purée: Peel and cut 1 sweet potato into 2-inch chunks. Toss the chunks into a large pot of boiling water and simmer until tender, 10 to 15 minutes. Remove from heat and drain. Using a handheld potato masher and large bowl, or a food processor, mash until smooth.

Cook the pasta according to the package instructions. In the last 2 minutes of the pasta’s cooking time, add the frozen peas.

Meanwhile, in a large heavy-bottomed saucepan, melt the butter over medium-low heat. Sprinkle the flour over the butter, stir and allow to cook for a minute or two. Now slowly add the milk, stirring continually to stop the sauce from lumping up. If it’s not thickening, nudge the heat up just a bit. Add the cheeses and stir as they melt. Add the puréed sweet potato and stir well to combine. Taste before seasoning with salt and pepper.

Drain the pasta and peas in a sieve. Pour the cooked pasta and peas into the pot with the sauce and give everything a good stir. Serve straight from the pot into bowls.